We took a car from Costa Adeje and drove up to mount Teide.
It just shows you a completely different side of Tenerife. There were forest national park areas on the way up - and worth stopping off for a wander as there were some fantastic views, not to mention kids playground and football pitch.
On Teide that views are just incredible - watch out for the temperature as it can get really cold, down to freezing, so you need to take a few layers.
I didn't take the cable car so can't comment on that.
Towards the top was a fairly inconspicious Visitor Centre. It didn't look much from the outside, however it's well worth a visit - there was a short film, plus loads of information about how the islands were formed - it was a good museum/information source. The visitor centre was free.
Note - There are loads of cyclists around - home from home a bit like Box Hill!
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